... Lebesgue differentiation theorem, it is easy to see that for anyf ∈ L1locRd,fx≤Nfx, 2.59 for μ − a.e. x ∈ Rd,see11 for details. By Lemmas 2.2–2.5, we haveb1,b2,Iα,2f1,f2Lq≤Nb1,b2,Iα,2f1,f2Lq≤M#,βb1,b2,Iα,2f1,f2Lq≤ ... ,ymmn−αdμy1···dμym. 1.4 For m 1, we denote Iα,1by Iα, which is the Riesz potential operator related to μ.Given m ∈ N, for all 1 ≤ j ≤ m, we denote by Cmjthe family ... rj 1 for some j,Iα,mf1, ,fmLs,∞μ≤ Cmj1fjLrjμ. 2.9Proof. The proof follows the idea that, for the classical setting, can be found in 4. For thesake...